Technological progress, organizational change and the size of the Human Resources Department

and the first-order conditions are given by:

β^t

- — β tμt = 0

ct

β^tμ_tw_th_t - βλt (1 - δ) Eth^δ (1 — T_t^s)^-δ = 0

^βt^+1μt+1 ^{(1 +} rt+i⁾ — ^βtμt = ⁰

β ^t+1μt+1Wt+1Tt^s+1 + β ^t+1λt+ιδEt+ιhδ^-1 (1 — Γ      — β ^tλ_t = 0

β^t [(1 + r_t) a_t + w_th_tT_t^s — c_t — a_t+i] = 0

β^{t h}Etht^δ (1 — Tt^s)^1-δ — ht+1ⁱ =0

from which, rearranging and substituting, we get the following relevant equations:

ɪ = ^β- (1+ r,+1)
^ct    ^ct+1

Wtht       = eôw^—Ts+^ ₊ βwt+1Tt^s+1

c_t (1 — δ) E_th_t^δ (1 — T_t^s)^-δ       ct+1 (1 — δ)           ct+1

at+1 =(1+rt) at + Wt htT_t^s — ct

ht+1 = Etht^δ (1 — Tt^s)^1-δ

Equation (9) is the typical Euler equation for optimal consumption over time.
Equation (10) is the optimality condition for human capital accumulation after sub-
stitution of the Lagrange multipliers λ_t and μ_t using the first-order conditions with
respect to consumption and production time supply notably. The left-hand side mea-
sures the marginal cost of human capital accumulation, which is simply reflected in
the wage forgone in period t due to education. The right-hand side is the sum of
two marginal benefit terms: the increase in the marginal productivity of education
time in t +1 and the increasing labour remuneration in the same period. Equations
(11) and (12) are just the law of evolution of consumer’s wealth and the education
technology respectively.

3.3 Market equilibrium conditions

Together with the solution of the problem of the firm and of the household, the
stationary equilibrium of the decentralized economy is characterized also by the
market equilibrium condition:

, ^{nξ (1} — Pt)θ ρ^η
yt = Ct +-------J-------

dt

15

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